What is the answer to ((-2+9i))/((-6+i)(s))=-1 ?

The answer to ((-2+9i))/((-6+i)(s))=-1 is s=-21/37+52/37 i

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((-2+9i))/((-6+i)(s))=-1

\frac{( - 2 + 9 i )}{( - 6 + i ) ( s )} = - 1

s = - \frac{21}{37} + \frac{52}{37} i

Solution steps

\frac{( - 2 + 9 i )}{( - 6 + i ) ( s )} = - 1

Substitute

s = x + y i

\frac{- 2 + 9 i}{( - 6 + i ) ( x + y i )} = - 1

Multiply both sides by

(- 6 + i) (x + y i)

\frac{- 2 + 9 i}{( - 6 + i ) ( x + y i )} (- 6 + i) (x + y i) = - 1 \cdot (- 6 + i) (x + y i)

Expand

- 2 + 9 i = (6 x + y) + i (- x + 6 y)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[- 2 = 6 x + y 9 = - x + 6 y]

[- 2 = 6 x + y 9 = - x + 6 y] : x = - \frac{21}{37}, y = \frac{52}{37}

Substitute back

s = x + y i

s = - \frac{21}{37} + \frac{52}{37} i

(z - i)^{2} = 2

r (t) = t i + t^{2} j + 2 t k, (2, 4, 4)

x^{2} + x + 1 + i = 0

x + i (y + 1) = 2 x + i 2 y

v = i r, r

What is the answer to ((-2+9i))/((-6+i)(s))=-1 ?
The answer to ((-2+9i))/((-6+i)(s))=-1 is s=-21/37+52/37 i